Epidural electrical stimulation (EES) of lumbosacral sensorimotor circuits improves leg motor control in animals and humans with spinal cord injury (SCI). Upper-limb motor control involves similar circuits, located in the cervical spinal cord, suggesting that EES could also improve arm and hand movements after quadriplegia. However, the ability of cervical EES to selectively modulate specific upper-limb motor nuclei remains unclear. Here, we combined a computational model of the cervical spinal cord with experiments in macaque monkeys to explore the mechanisms of upper-limb motoneuron recruitment with EES and characterize the selectivity of cervical interfaces. We show that lateral electrodes produce a segmental recruitment of arm motoneurons mediated by the direct activation of sensory afferents, and that muscle responses to EES are modulated during movement. Intraoperative recordings suggested similar properties in humans at rest. These modelling and experimental results can be applied for the development of neurotechnologies designed for the improvement of arm and hand control in humans with quadriplegia.